Fourth-Order Differential Equation with Deviating Argument. (18th March 2012)

• Record Type: Journal Article
• Authors: Bartušek, M.; Cecchi, M.; Došlá, Z.; Marini, M.
• Other Names: Eloe Paul Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-03-18
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/185242
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We consider the fourth-order differential equation with middle-term and deviating argument x ( 4 ) ( t ) + q ( t ) x ( 2 ) ( t ) + r ( t ) f ( x ( φ ( t ) ) ) = 0, in case when the corresponding second-order equation h ″ + q ( t ) h = 0 is oscillatory. Necessary and sufficient conditions for the existence of bounded and unbounded asymptotically linear solutions are given. The roles of the deviating argument and the nonlinearity are explained, too.